Even the ones in the museums look like this - I would leave it alone and chalk it up to age.

I've had good luck using automotive rubbing compound to rub out marks and renew the shine on old plastics.

Try an oil soap or distilled alcohol in a small area.

try a regular white eraser. mr. clean magic eraser strips the finish off of things, and I'd be really scared. pink pet erasers sometimes leave little pink streaks. plain white pencil erasers will take the scuff marks off of just about anything (shoes, too!).

I have used Simple Green with good effect on plastic Elephant Stools. I think I bought the stuff at Target. It's a relatively mild all-purpose cleaner that cuts through grime. Spray it, rinse it off--no scrubbing. Not sure if it will cut through the scuffs. Of course, you should alway test it out on a hidden area to be certain that it does not ruin the plastic. There are also some automobile products out there, but they tend to leave a film that can cause damage to certain plastics when exposed to light.

I am also a fan of Simple Green!

Yes! Simple Green has gotten horrible black marks off my walls after renovation ... give it a try!

soapy cloroxy water and a rag... get to scrubbin'!

kartell sells their own plastic cleaner

A product called Novus plastic polish is EXACTLY what you need. It comes in three grades of abrasiveness, and you'd probably get the most benefit out of No. 2. I use it on flea-market finds all the time, and it transforms them.

I think some hardware stores carry it; I order it by mail. Google "Novus plastic polish" and you'll find many sources.

Sometimes Goo Gone works on scuff marks.

I'd try a Magic Eraser on an inconspicuous spot first to see if it affects the finish at all.

I cleaned up a REALLY badly black-scuffed Kartell Componibili with a Magic Eraser, and it looks good as new now.

(But yes, Kartell does make a plastic cleaner, as beakllerina mentioned!)

Plastic is sandable. Start with a 600 grit. I second the automotive rubbing compound. Once you've got the scratches and marks out sanded out use a compound and a car buffer. I've gotten a high gloss sheen out of scuffed up plastic with this method.

You can have pieces gel coated as well. I've seen that recommended for older plastic furniture, especially if the plastic has yellowed or stained.

I have 4 of these chairs from the 70's. They look great! I once used a regular paste wax and buffed them. Make sure its the kind that won't yellow, since your chair is white.

Buffy

I wouldn't try simple green on white plastic, it leaves a greenish tone on the plastic. Start with 409 to get rid of the easier smudges, if there's any left try 'bleche white', you can find it at car part stores like Kragen, ultimately ajax for all those stubborn marks, scrubing with a non-abrasive scotch brite pad. When all marks are gone polish with Meguiar's PlastX to restore the plastic shine